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Two frameworks for pricing defaultable derivatives

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  • Zaevski, Tsvetelin S.
  • Kounchev, Ognyan
  • Savov, Mladen

Abstract

The purpose of this paper is to present two essentially different schemes for deriving the partial differential equations (PDE) for the price of the so-called defaultable derivatives. In the first one the asset price is represented as a solution of a stochastic differential equation (SDE), stopped at a stochastic time. The second one explores the idea of adding a jump process assuming that the stopping time is the moment of its first jump. We investigate also the role of the loss rate, which represents the loss of the asset at the default moment. In both cases we examine various assumptions and dependencies between the underlying asset, the stopping time, and the loss rate. We examine separately the cases when the underlying asset price is driven by a Brownian motion or by a Lévy process.

Suggested Citation

  • Zaevski, Tsvetelin S. & Kounchev, Ognyan & Savov, Mladen, 2019. "Two frameworks for pricing defaultable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 309-319.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:309-319
    DOI: 10.1016/j.chaos.2019.04.025
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    More about this item

    Keywords

    Stopping times; Default; Risk-neutral measure; Asset pricing; Derivative pricing; Convertible bonds;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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